Midterm Exam, CSCI 385, Fall 2014

• Please answer each question carefully and thoughtfully. You need to demonstrate that you understand the material covered.
• Use as many pages as you wish, but make sure that you label each answer with the question number.
• Please write neatly, and print if possible. If I can't read your answer, it is incorrect.
• Please make sure that you answer all parts of the questions.
• For each answer, justify you answer with a short argument or explain any mathematical expression, A simple Yes is wrong.

1. Asymptotic Notation
   1. [2 points] State the definition of f(n) ∈ O(g(n))
   2. [1 points] is n² + 3n +1 ∈ O(n³)?
   3. [1 points] is n² + 3n +1 ∈ Ω(n³)?
   4. [2 points] is n² + 3n +1 ∈ Θ(n³)?
   5. [3 points] Describe the strengths and weekness of classifying an algorithm using asymptotic notation.

2. Lists vs arrays
   1. [4 points] What are basic operations on an ordered array/list?
   2. [3 points] What are the performance expectations for these operations on an ordered array?
   3. [3 points] What are the performance expectations for the operations on an ordered list?
   4. [4 points] Describe guidelines for selecting the proper data structure (list or array) for a problem.

3. Polynomial Evaluation

   The array A[0..n] contains the coefficients a₀, a₁ ... a_n for the polynomial a_nxⁿ+ a_n-1x^n-1+ ... + a₁x¹+a₀.

   1. [4 points] Give an algorithm to evaluate the polynomial at a given point (x=4 for example.)
   2. [2 point] What is the measure of the input size for your algorithm?
   3. [2 point] What is the basic operation in your algorithm?
   4. [3 points] Give an expression which represents the timing function of your algorithm, make sure to label each term of the expression with the associated line number.
   5. [2 points] What is the performance class of your algorithm?

   
   
   
   More questions on back.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

4. Recursion Consider the following algorithm:

   RPM(n, m, sum)
   
    if n = 1 then
        return m+sum
    elseif n is even  then
        return RPM(n/2, m*2, sum)
    else 
        return RPM((n-1)/2, m*2, sum+m)
   
       

   1. [2 points] What does this algorithm do?
   2. [2 points] What is the measure of the input size for this algorithm?
   3. [2 points] What is the critical operation for this algorithm?
   4. [3 points] Provide a timing function directly related to the algorithm. (Include line numbers).
   5. [3 points] Derive a closed form of the timing function. (Show steps)
   6. [2 points] What is the performance class of this algorithm?